This invention relates to the conversion of digital data to an analog signal. Digital data is frequently stored on a storage medium as a series of digital words of fixed length. The finite nature of the word length is a primary limitation on the fidelity of the audio output. It follows from this limitation that the number of output states is limited to 2.sup.n, where n represents the number of bits in the stored digital word. Therefore, a 16 bit A/D converter can represent 65,536 output states. The resolution of this A/D converter is therefore 1/65,536. In practice, this means that if an analog signal changes by an amount smaller than the resolution of the converter, both signals will be assigned the same digital word. In theory, the higher the resolution (using a higher n value), the higher the fidelity of the converted output signal to the quantized input signal. In applications such as digital audio, for example, nonlinearities in the conversion from digital to analog create distortion that is primarily audible as noise at low levels. One example of such noise is zero-cross distortion. The zerocross distortion caused by the switching of LSBs causes distortion to appear as higher frequency signals at multiples of the input frequency.
In an effort to improve the accuracy of conversion, some manufacturers have resorted to converting 16 bit digital data by oversampling the data, that is sampling the digital data at a multiple of the input sampling frequency. This results in a word length higher than that of the stored word length. The most significant bits are then converted and the least significant bits are either rounded off or used in noise shaping circuits to enhance the linearity of low amplitude signals, as they contain amplitude information below that contained by the most significant bits. Linearity measures the ability of the converter to output a signal proportional to the level of the signal prior to quantization. In a perfect D/A converter, a change of 1 LSB corresponds exactly to a change of 1/2.sup.n of the Full Scale value used to quantize the input analog signal.
The compact disk (CD) system utilizes a format wherein digital data is stored as 16 bit words sampled at 44.1 Khz. Recently, converters utilizing 18 or 20 bit (or higher) architectures have been employed to provide a more accurate conversion of the 16 bit data words stored on the compact disk. One such converter is disclosed in Japanese patent publication Sho 55-28445 which utilizes a "noise shaping" circuit that uses 18 or 20 bit data to decrease the low signal level distortion present in decoded audio signals. However, even this "noise shaping" scheme has the effect of increasing high frequency noise at low amplitude levels, thereby impairing sound quality.
When the LSB switches from one state to another as the amplitude of the signal changes, the converted signal resembles a square wave whose amplitude, in the time domain, is determined by the resolution of the converter divided by the Full Scale value of the analog input signal. The width of this square wave is determined by the rate of change of the analog input signal, that is, its frequency. This square wave, being the decoded LSB signal, represents low level signals. However, due to its shape, its spectral content is determined by a sum of sinusoids determined by the Fourier decomposition of the signal. These sinusoids are of higher frequency than the input signal and are heard as high frequency noise in the decoded analog signal. This distortion is unwanted and impairs the quality of the recovered sound.